Assembling Molecules in Atomix is Hard

It is shown that assembling molecules in the Atomix game can be used to simulate finite automata. In particular, an instance of Atomix is constructed that has a solution if and only if the non-emptiness intersection problem for finite automata is solvable. This shows that the game under consideration is PSPACE-complete, improving a recent result of Hueffner et al. Thus, there are Atomix games which have superpolynomially long optimal solutions. We also give an easy construction of Atomix game levels whose optimal solutions meet the worst case.     «

It is shown that assembling molecules in the Atomix game can be used to simulate finite automata. In particular, an instance of Atomix is constructed that has a solution if and only if the non-emptiness intersection problem for finite automata is solvable. This shows that the game under consideration is PSPACE-complete, improving a recent result of Hueffner et al. Thus, there are Atomix games which have superpolynomially long optimal solutions. We also give an easy construction of Atomix game le...     »